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Theorem caov411d 6499
 Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovd.1
caovd.2
caovd.3
caovd.com
caovd.ass
caovd.4
caovd.cl
Assertion
Ref Expression
caov411d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov411d
StepHypRef Expression
1 caovd.2 . . 3
2 caovd.1 . . 3
3 caovd.3 . . 3
4 caovd.com . . 3
5 caovd.ass . . 3
6 caovd.4 . . 3
7 caovd.cl . . 3
81, 2, 3, 4, 5, 6, 7caov4d 6498 . 2
94, 1, 2caovcomd 6470 . . 3
109oveq1d 6311 . 2
114, 1, 3caovcomd 6470 . . 3
1211oveq1d 6311 . 2
138, 10, 123eqtr3d 2506 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 973   wceq 1395   wcel 1819  (class class class)co 6296 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-iota 5557  df-fv 5602  df-ov 6299 This theorem is referenced by: (None)
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